In this work, we build on [1]}, [2]} and propose a synergistic offline-online framework to approach an optimal solution. We combine the baseline offline controller in [1]} with a novel online controller and refinement procedure that improves the baseline guarantees as new data is collected. The synergy arises from the online controller using the offline abstraction along with the current state and new data to choose the next best action. The online controller improves the baseline guarantees by avoiding the discretization error and reducing regression error as new data is collected. The new data are also used to refine the abstraction and offline controller via local GP regression, which significantly reduces the computation overhead, enabling online computations.
